Combine the flour, sugar, cinnamon and nutmeg in a small bowl. Add 8 tablespoons of the melted butter and combine until crumbly. Refrigerate for 15 minutes.
Slice a very thin piece off the bottom of each peach half so they have flat bottoms. Brush the bottom and sides of a 9- by 11-inch baking dish with some of the remaining 3 tablespoons of melted butter, and then brush the rest of the butter on the peaches. Place the peaches in the pan cut-side up and about an inch or so apart. Sprinkle a little bit of salt on the peaches. Top each peach with some of the streusel. Bake in the oven until the peaches are soft and the streusel is lightly golden brown, 45 to 55 minutes, depending on how ripe the peaches are.
When the peaches are almost done, put the syrup in a small saucepan and bring to a simmer on low heat, Keep warm. Serve the peaches drizzled with some of the syrup and topped with whipped cream, if using.